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Single mode squeezing for Interferometry beyond shot noise . Bernd Lücke J. Peise , M. Scherer, J. Kruse, O. Topic, W. Ertmer , C. Klempt Institute of Quantum Optics, Leibniz Universität Hannover, Germany G. Gebreyesus , F. Deuretzbacher , L. Santos - PowerPoint PPT Presentation
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QUEST - Centre for Quantum Engineering and Space-Time Research
Single mode squeezing for Interferometry beyond shot noise
Bernd Lücke
J. Peise, M. Scherer, J. Kruse, O. Topic, W. Ertmer, C. KlemptInstitute of Quantum Optics, Leibniz Universität Hannover, Germany
G. Gebreyesus, F. Deuretzbacher, L. SantosInstitute of Theoretical Physics , Leibniz Universität Hannover, Germany
J. ArltQUANTOP, Institut for Fysik og Astronomi, Aarhus Universitet, Denmark
P. Hyllus, A. SmerziINO-CNR BEC Center and Dipartimento di Fisica, Universita‘ di Trento, Italy
L. PezzeLaboratoire Charles Fabry, Institut d’Optique, 91127 Palaiseau, France
QUEST - Centre for Quantum Engineering and Space-Time Research
A typical interferometer
Counter
| α >
θ
θest
| 0 >
N-1
N+1
π 2π 3πθ
< N
+1 -
N-1 >
S
θest2
QUEST - Centre for Quantum Engineering and Space-Time Research
The origin of shot noise
-5 -3 -1 +1 +3 +5
coun
ts
7
6
5
4
3
2
1
N+1 - N-1
3
QUEST - Centre for Quantum Engineering and Space-Time Research
The origin of shot noise
+1
+1
+1
-1
+1
+3
coun
ts
7
6
5
4
3
2
1
N+1 - N-1
-5 -3 -1 +1 +3 +5
4
QUEST - Centre for Quantum Engineering and Space-Time Research
The origin of shot noise
coun
ts
7
6
5
4
3
2
1
-1
-1
+1
-1
+1
-1 N+1 - N-1
-5 -3 -1 +1 +3 +5
5
QUEST - Centre for Quantum Engineering and Space-Time Research
The origin of shot noise
coun
ts
7
6
5
4
3
2
1
N
N+1 - N-1
-5 -3 -1 +1 +3 +5
6
QUEST - Centre for Quantum Engineering and Space-Time Research
Shot noise limited sensitivity
π 2π 3π
θ
< N
+1 -
N-1 >
NNN
SS
est1
/
S
θest
7
QUEST - Centre for Quantum Engineering and Space-Time Research
How can you beat this limit?
uncorrelated particles
shot-noise limit
entangled particles
Heisenberg limitNest1
Nest1
8
QUEST - Centre for Quantum Engineering and Space-Time Research
Twin-Fock interferometer
Introduction
outline
N| N||
Fock state interferometerN| N||
9
QUEST - Centre for Quantum Engineering and Space-Time Research
Spin dynamics as a source of entanglement
mF: -1 0 +1
2nd quantization 1st quantization
1,1|| ,|,|~|
10
QUEST - Centre for Quantum Engineering and Space-Time Research
Measuring sub shot-noise fluctuations
shot noise
detection noise
total number of atoms
stan
dard
dev
iatio
n/2
• 7dB below shot noise @ 8000 atoms• detection noise σ(Jz) = 20 atoms
11
QUEST - Centre for Quantum Engineering and Space-Time Research
σJz
ΦJz= (N-1 - N+1)/2
σΦ
Jx
Jy
Representation on the generalized Bloch sphere
RF
Entangled Twin-Fock stateproduced using spin dynamics
12
coherent superpositionproduced using rf preparation
Jz
Jx
Jy
σJz=0
QUEST - Centre for Quantum Engineering and Space-Time Research
Uncorrelated input vs. Twin-Fock input
13
QUEST - Centre for Quantum Engineering and Space-Time Research
Output signal
14
QUEST - Centre for Quantum Engineering and Space-Time Research
Sensitivity
15
QUEST - Centre for Quantum Engineering and Space-Time Research
Twin-Fock interferometer
Introduction
outline
N| N||
Fock state interferometerN| N||
16
QUEST - Centre for Quantum Engineering and Space-Time Research
01 NNN total
NN ,|
2,| NN
NnCNn
n ,|||
Counter
| NN total|
N|
CounterN|-1
0
+1
17
QUEST - Centre for Quantum Engineering and Space-Time Research
Does it work with two different Fock states?
NN ,|
2,| NN
Jz = (N
+1 - N-1 )/2
counts
Jz = (N
+1 - N-1 )/2
18
QUEST - Centre for Quantum Engineering and Space-Time Research
Does it work with a coherent and a Fock input state?
Counter
|
N|
11 NNN total
NN total|
NnCNn
n ,|||
NmNn est 2
2
NnnNmest
21
Ultrasensitive Atomic clock with single-mode number-squeezing,L. Pezzé and A. Smerzi, arXiv:1004.5486v1
19
QUEST - Centre for Quantum Engineering and Space-Time Research
Measuring a single output port
Counter
|
N|
coun
ts
N+1N
θ = 0
N+1N
θ<< π
N+1N
Θ = π
|α|²
QUEST - Centre for Quantum Engineering and Space-Time Research
Sub shot-noise sensitivity can be achieved with Twin-Fock states produced by spin dynamics
For sub shot-noise sensitivity entanglement is necessary
summary
N| N||
A single Fock state and an coherent input state are also suitable for sub shot-noise interferometryN| N||
21
QUEST - Centre for Quantum Engineering and Space-Time Research
Thank you for your attention.
22
W.Ertmer I.Geisel C.Klempt J.Peise B.Lücke J.Mahnke S.Coleman
QUEST - Centre for Quantum Engineering and Space-Time Research
Phase estimation for θ=π/2co
unts
Jz = (N+1 - N-1)/2co
unts
Jz = (N+1 - N-1)/2
coherent input state Twin-Fock input state
QUEST - Centre for Quantum Engineering and Space-Time Research
Phase estimation for θ=π/2co
unts
Jz = (N+1 - N-1)/2co
unts
Jz = (N+1 - N-1)/2
coherent input state Twin-Fock input state
QUEST - Centre for Quantum Engineering and Space-Time Research
Phase estimation for θ=π/2co
unts
Jz = (N+1 - N-1)/2co
unts
Jz = (N+1 - N-1)/2
coherent input state Twin-Fock input state
QUEST - Centre for Quantum Engineering and Space-Time Research
Actual measurement
-1 0
6
4
2
0
coherent input state Twin-Fock input state
1(N+1 - N-1)/N
QUEST - Centre for Quantum Engineering and Space-Time Research
Jz
JyJx
The gerneralized Bloch sphere
Multi particle Bloch sphere:
Jx (a† b + a b†)/2 Jy = -i (a† b - a b†)/2 with Jz = (N+1 - N-1)/2 Jz (a† a - b† b)/2
QUEST - Centre for Quantum Engineering and Space-Time Research
Expension of the state reveals its entanglement
NnCNn
n ,|||
Why is this state not entangled?
nmCC nnm
m ,||| ,,
,
2,0|1,1|0,2|2 2,0,1,1,0,2, CCCCCCnm
Because…
In 1st quantization: ||||~|